Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.
We study non-Hermitian (NH) fermionic superfluidity subject to dissipation of Cooper pairs on a honeycomb lattice, for which we analyze the attractive Hubbard model with a complex-valued interaction. Remarkably, we demonstrate the emergence of the dissipation-induced superfluid phase that is anomalously enlarged by a cusp on the phase boundary. We find that this unconventional phase transition originates from the interplay between exceptional lines and Van Hove singularity, which has no counterpart in equilibrium. Moreover, we demonstrate that the infinitesimal dissipation induces the nontrivial superfluid solution at the critical point. Our results can be tested in ultracold atoms with photoassociation techniques by postselecting special measurement outcomes with the use of quantum-gas microscopy, and they can lead to an understanding of the NH many-body physics triggered by exceptional manifolds in open quantum systems.
Recently, the influence of dissipation on a quantum system has attracted much attention, particularly on how the non-Hermitian terms modify the energy spectrum, band topology, and phase transition point. Motivated by the recent investigation of non-Hermitian
s-wave superfluidity, we study the non-Hermitian chiral
p+ip superfluid (SF) with a complex-valued interaction, originating from inelastic scattering between fermions. We reformulate the non-Hermitian mean-field theory for chiral SFs and derive the gap equation in the path integral approach. By numerically solving the gap equation, we obtain the phase diagram of the non-Hermitian
p+ip SF, characterized by the reentrant SF transition and dissipation-induced SF phase, as a result of the evolution of the exceptional lines. The method can be extended to higher partial-wave chiral SFs, such as
d+id and
f+if-wave SFs. We further consider such a chiral
p+ip SF on a square lattice, to investigate the influence of dissipation on topology. We find that the non-Hermitian skin effect is absent in the specific cylinder geometry, in which the topology associated with the edge modes and Chern number is robust to dissipation. Besides, we find that the energies at the robust point nodes and line nodes are pure real. We further verify the conditions of zero winding number in (quasi-) one-dimensional systems, and prove an associated ``no-go'' theorem, which is hopefully applied to explore the geometry dependent skin effect.
The Higgs and Nambu-Goldstone modes are paradigmatic collective excitations in superconductors and superfluids. These modes are commonly analyzed within the pseudospin formulation of BCS theory, where the dynamics are obtained from the Heisenberg equations of motion for pseudospins. However, this construction becomes inconsistent when directly extended to non-Hermitian systems. In this work, we develop a consistent pseudospin framework for non-Hermitian fermionic superfluids based on the metricized formulation of non-Hermitian quantum mechanics. We apply this formalism to a driven non-Hermitian BCS-type Hamiltonian with complex pairing interaction and analyze its collective excitation spectrum. We find that, in addition to the conventional Higgs (amplitude) mode, the system hosts a novel phase mode that has no counterpart in Hermitian superfluids. Remarkably, this mode is gapped even in the absence of the Anderson-Higgs mechanism, as is the case in neutral superfluids. Furthermore, the resonance spectrum depends explicitly on the initial nongauge phase of the complex order parameter and the dynamical response remains finite at resonance, in contrast to the divergence characteristic of Hermitian systems. These resonances disappear upon the emergence of exceptional points.